CHIME: Clustering of high-dimensional Gaussian mixtures with EM algorithm and its optimality

Cai, Tianxi; Ma, Jing; Zhang, Linjun

doi:10.1214/18-aos1711

Cited by 58 publications

(62 citation statements)

References 27 publications

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“…The 2D images of 89 cross sections (89 CS), 92 cross sections (95 CS), and 95 cross sections (95 CS) in the T1-weighted brain MRI image were selected for segmentation. The comparison algorithms used were FCM, CoFKM (Cai et al, 2019), two-layer automatic weighted clustering algorithm (TW-k-means) (Singh et al, 2020), multitask-based K-means (CombKM) (Chen et al, 2013), and collaborative clustering based on sample and feature space (coclustering) (Gu and Zhou, 2009). In the experiment, the iteration stop threshold ε of each algorithm is set to 0.001, and the maximum number of iterations l was set to 100.…”

Section: Simulation Experiments Analysis Experimental Backgroundmentioning

confidence: 99%

A Novel Brain MRI Image Segmentation Method Using an Improved Multi-View Fuzzy c-Means Clustering Algorithm

Lee

et al. 2021

Front. Neurosci.

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Background: The brain magnetic resonance imaging (MRI) image segmentation method mainly refers to the division of brain tissue, which can be divided into tissue parts such as white matter (WM), gray matter (GM), and cerebrospinal fluid (CSF). The segmentation results can provide a basis for medical image registration, 3D reconstruction, and visualization. Generally, MRI images have defects such as partial volume effects, uneven grayscale, and noise. Therefore, in practical applications, the segmentation of brain MRI images has difficulty obtaining high accuracy.Materials and Methods: The fuzzy clustering algorithm establishes the expression of the uncertainty of the sample category and can describe the ambiguity brought by the partial volume effect to the brain MRI image, so it is very suitable for brain MRI image segmentation (B-MRI-IS). The classic fuzzy c-means (FCM) algorithm is extremely sensitive to noise and offset fields. If the algorithm is used directly to segment the brain MRI image, the ideal segmentation result cannot be obtained. Accordingly, considering the defects of MRI medical images, this study uses an improved multiview FCM clustering algorithm (IMV-FCM) to improve the algorithm’s segmentation accuracy of brain images. IMV-FCM uses a view weight adaptive learning mechanism so that each view obtains the optimal weight according to its cluster contribution. The final division result is obtained through the view ensemble method. Under the view weight adaptive learning mechanism, the coordination between various views is more flexible, and each view can be adaptively learned to achieve better clustering effects.Results: The segmentation results of a large number of brain MRI images show that IMV-FCM has better segmentation performance and can accurately segment brain tissue. Compared with several related clustering algorithms, the IMV-FCM algorithm has better adaptability and better clustering performance.

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Section: Simulation Experiments Analysis Experimental Backgroundmentioning

confidence: 99%

A Novel Brain MRI Image Segmentation Method Using an Improved Multi-View Fuzzy c-Means Clustering Algorithm

Lee

et al. 2021

Front. Neurosci.

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“…Furthermore, we also assume that the eigenvalues of the covariance matrix Σ are bounded from below and above. This assumption is commonly used in high dimensional statistics, ranging from high dimensional linear regression (Javanmard and Montanari, ), covariance matrix estimation (Cai and Yuan, ), classification (Cai and Liu, ) and clustering (Cai et al ., ).…”

Section: Introductionmentioning

confidence: 97%

High Dimensional Linear Discriminant Analysis: Optimality, Adaptive Algorithm and Missing Data

Cai

Zhang

2019

Journal of the Royal Statistical Society Series B: Statistical Methodology

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Summary The paper develops optimality theory for linear discriminant analysis in the high dimensional setting. A data‐driven and tuning‐free classification rule, which is based on an adaptive constrained l1‐minimization approach, is proposed and analysed. Minimax lower bounds are obtained and this classification rule is shown to be simultaneously rate optimal over a collection of parameter spaces. In addition, we consider classification with incomplete data under the missingness completely at random model. An adaptive classifier with theoretical guarantees is introduced and the optimal rate of convergence for high dimensional linear discriminant analysis under the missingness completely at random model is established. The technical analysis for the case of missing data is much more challenging than that for complete data. We establish a large deviation result for the generalized sample covariance matrix, which serves as a key technical tool and can be of independent interest. An application to lung cancer and leukaemia studies is also discussed.

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“…Despite the recent progress, we are not aware of any results that characterize the local convergence behavior of the EM algorithm on mixtures of two or more Gaussians. For variants of the EM algorithm for fitting high-dimensional mixture models, we refer readers to Dasgupta and Schulman [10], Cai, Ma and Zhang [6], Wang et al [28], Yi and Caramanis [32].…”

Section: Related Workmentioning

confidence: 99%

Statistical convergence of the EM algorithm on Gaussian mixture models

Zhao¹,

Li²,

Sun³

2020

Electron. J. Statist.

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We study the convergence behavior of the Expectation Maximization (EM) algorithm on Gaussian mixture models with an arbitrary number of mixture components and mixing weights. We show that as long as the means of the components are separated by at least Ω( min{M, d}), where M is the number of components and d is the dimension, the EM algorithm converges locally to the global optimum of the log-likelihood. Further, we show that the convergence rate is linear and characterize the size of the basin of attraction to the global optimum.MSC 2010 subject classifications: Primary 62F10, ; secondary 65K05.

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CHIME: Clustering of high-dimensional Gaussian mixtures with EM algorithm and its optimality

Cited by 58 publications

References 27 publications

A Novel Brain MRI Image Segmentation Method Using an Improved Multi-View Fuzzy c-Means Clustering Algorithm

A Novel Brain MRI Image Segmentation Method Using an Improved Multi-View Fuzzy c-Means Clustering Algorithm

High Dimensional Linear Discriminant Analysis: Optimality, Adaptive Algorithm and Missing Data

Statistical convergence of the EM algorithm on Gaussian mixture models

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